In this paper, we present a characteristic set method for mixed differential and difference polynomial systems. We introduce the concepts of coherent, regular, proper irreducible, and strongly irreducible ascending chains and study their properties. We give an algorithm which can be used to decompose the zero set for a finitely generated differential and difference polynomial set into the union of the zero sets of regular and consistent ascending chains. As a consequence, we solve the perfect ideal membership problem for differential and difference polynomials.

Authors: Xiao-Shan Gao, Joris van der Hoeven, Chunming Yuan, Guilin Zhang

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